You’ll need to make a silicone mold of the piece. A hard rubber mold may damage delicate structures and, we used to lead solder the sprue to the item which could leave a mark. There will be some shrinkage with either method so, it's won’t be identical. You can also carve a wax just like the existing piece and cast that wax and add the engravings from a mold. Jewelry schools can do it, and any companies that do ‘lost wax casting’ can do it. Be careful with soft stones (pearls, emeralds, etc.). Once you have the mold, you can make some for other family members.